随时蒙特卡洛

IF 2.4 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Lawrence M. Murray, Sumeetpal S. Singh, Anthony Lee
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引用次数: 4

摘要

摘要蒙特卡罗算法模拟一些规定数量的样本,取一些随机的实时时间来完成必要的计算。这项工作考虑了相反的情况:在计算中施加实时预算,这导致模拟样本的数量是随机的。更复杂的是,每次模拟所需的实时时间可能取决于产生的样本,因此样本本身并不独立于它们的数量,并且相对于计算时间的长度偏差是明显的。当使用马尔可夫链蒙特卡罗(MCMC)算法并且需要马尔可夫链的最终状态(而不是所有状态的平均值)时,这尤其成问题,这就是MCMC并行回火实现的情况。在这种情况下,长度偏差不会随着计算预算的增加而减少。在序列蒙特卡罗(SMC)算法中也会出现这种情况,这是本文研究的重点。为了解决这个问题,我们提出了一个随时框架,使用连续时间马尔可夫跳跃过程来实时研究计算过程。我们首先证明,对于任何MCMC算法,由于强加的实时计算预算,最终状态分布的长度偏差可以通过使用多链结构来消除。然后在大规模SMC${}^2 $实现上演示了这种结构的效用,该实现使用分布在亚马逊EC2服务上的128个图形处理单元集群上的40亿个粒子。anytime框架在SMC${}^2 $算法中对MCMC移动步骤施加实时预算,确保所有处理器同时为重采样步骤做好准备,明显地减少了空闲到适当的等待时间,并提供了对总计算预算的实质性控制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Anytime Monte Carlo
Abstract Monte Carlo algorithms simulates some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the number of samples simulated being random. To complicate matters, the real time taken for each simulation may depend on the sample produced, so that the samples themselves are not independent of their number, and a length bias with respect to compute time is apparent. This is especially problematic when a Markov chain Monte Carlo (MCMC) algorithm is used and the final state of the Markov chain—rather than an average over all states—is required, which is the case in parallel tempering implementations of MCMC. The length bias does not diminish with the compute budget in this case. It also occurs in sequential Monte Carlo (SMC) algorithms, which is the focus of this paper. We propose an anytime framework to address the concern, using a continuous-time Markov jump process to study the progress of the computation in real time. We first show that for any MCMC algorithm, the length bias of the final state’s distribution due to the imposed real-time computing budget can be eliminated by using a multiple chain construction. The utility of this construction is then demonstrated on a large-scale SMC$ {}^2 $ implementation, using four billion particles distributed across a cluster of 128 graphics processing units on the Amazon EC2 service. The anytime framework imposes a real-time budget on the MCMC move steps within the SMC$ {}^2 $ algorithm, ensuring that all processors are simultaneously ready for the resampling step, demonstrably reducing idleness to due waiting times and providing substantial control over the total compute budget.
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来源期刊
DataCentric Engineering
DataCentric Engineering Engineering-General Engineering
CiteScore
5.60
自引率
0.00%
发文量
26
审稿时长
12 weeks
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